ROCKET EQUATIONS (VI)
Matlab Implementation of Euler method in Rocket equation
If you're new to my blog, Welcome!! For a better understanding kindly go through the blogs of this series.
Till far we talked about the aerodynamic forces, systems working in a rocket, derivation of ideal equations, switching into real conditions, and numerical approximation.
Rocket science is crucial for the development of space exploration and satellite technology. The field of rocket science requires a strong background in Mathematics, Physics, and Engineering, as well as a deep understanding of the complex interactions between the various components of a rocket and the physical environment in which it operates.
Numerical solutions play a crucial role in the design and analysis of rocket trajectories. The Euler method is easy and computationally inexpensive. It helps to gain a better understanding of the performance and behavior of rocket systems and make informed decisions about the design and operation of these systems. As we saw the final set of equations it’s quite evident that it is non-linear and complicated. Because of the complex nature of these equations, we fail to find an analytic solution, so we opt for the numerical solution to these problems. The numerical solution of rocket equations is an important tool in the design and analysis of rocket missions, as it allows engineers to predict the performance of a rocket and make necessary adjustments to ensure a successful mission.
In my last blog, I have given the numerical approximation for the rocket velocity using the Euler method and also discussed its stability(visible from the graph).
Below I have applied the MATLAB code and attached the results (below) which show its validity.
Below is my resulting graph.
“h” is the stepsize which makes the range from 0 to 1.
The initial velocity $v_{0}$ is set at $t=0$.
‘f’ is the right-hand side of our rocket equation, isolating (dv/dt) on one side. It takes the current velocity.
Here $v_{i}$ and $t_{i}$ as inputs.
This is perhaps my last blog on rocketry. If you guys are interested in some particular aspect lemme know in the comment section, and I will try to cover those. You can always let me know your views through comments or connect with me via LinkedIn. Next Monday I will be back with another blog. Till then bye-bye!
